How to remove the first address from the list?

The reason it shows the primary billing address as well is so you can still select it as an option if you’ve maybe selected a secondary address and then want to go back.

If you still wanted to remove it. You can remove it by filtering on the checkout fields.

I think something like this would work

add_filter( 'woocommerce_checkout_fields', function ( $fields ) {
	if ( isset( $fields['billing']['billing_address_book']['options']['billing'] ) ) {
		unset( $fields['billing']['billing_address_book']['options']['billing'] );
	}
	return $fields;
}, 10000, 1 );